The only way to do this is to check the origin and referrer headers.
Unfortunately, server to server this can't be done reliably as the referrer and origin headers would be set by the coder and so can be spoofed easily. For server to server calls you would be better off whitelisting IP addresses that are allowed to make calls to your APIS. In this case use something like How to get Real IP from Visitor? to get the real IP of the server and verify it against whitelisted IPs.
Assuming this is a JS call in browser and not server to server, and that you trust the browser, the only way this can really be done is by verifying the referrer and origin headers. This can still be spoofed with a browser plugin or even with a tool like Postman so I don't recommend it for high security. Here is a PHP example for verifying the origin or referrer.
$origin_url = $_SERVER['HTTP_ORIGIN'] ?? $_SERVER['HTTP_REFERER'];
$allowed_origins = ['example.com', 'gagh.biz']; // replace with query for domains.
$request_host = parse_url($origin_url, PHP_URL_HOST);
$host_domain = implode('.', array_slice(explode('.', $request_host), -2));
if (! in_array($host_domain, $allowed_origins, false)) {
header('HTTP/1.0 403 Forbidden');
die('You are not allowed to access this.');
}
Optionally also CORS headers are good as commented by @ADyson Cross-Origin Request Headers(CORS) with PHP headers